### ASA 126th Meeting Denver 1993 October 4-8

## 2pPA4. A new explanation for the double resonance of a pure vapor bubble.

**Yi Mao
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*Dept. of Phys. and Astron., Univ. of Mississippi, University, MS 38677
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**Lawrence A. Crum
Ronald A. Roy
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*Univ. of Washington, Seattle, WA 98105
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The second resonance frequency f[sub 0][sup (2)] of a pure bubble appeared
first in R. D. Finch and E. A. Nippiras' theoretical analysis [J. Acoust. Soc.
Am. 53, 1402--1410 (1973)]. However, no one has been able to observe a vapor
bubble oscillating at f[sub 0][sup (2)]. A new analysis based on numerical
calculations shows that f[sub 0][sup (2)] is physically unstable. By
analogizing bubble oscillations with those of a mass-spring system, it is found
that the resonance frequency F(f[sub d]) depends on the driving frequency f[sub
d] and the real bubble resonance f[sub 0][sup (2)] is a solution of F(f[sub
d])=f[sub d]. The behavior of F(f[sub d]) near f[sub d]=f[sub 0][sup (2)] shows
that the bubble tends to shift its oscillation frequency away from f[sub 0][sup
(2)] (repulsive); whereas F(f[sub d]) near the ordinary resonance f[sub 0][sup
(1)] is attractive. A theory developed by the authors for directly calculating
the resonance frequency and the damping constant without using the mass-spring
analogy gives only f[sub 0][sup (1)]. Therefore, we are forced to the
conclusion that f[sub 0][sup (2)] results from an improper mass-spring analogy
and is not physically observable. [Work supported by ONR.]